Purée 1 cup pistachios in a food processor until a thick paste forms. Add garlic, oil, 1 teaspoon salt, pepper, 1 cup chopped mint, and dill and purée until the mint is finely chopped and a thick sauce has formed.
Whisk labneh, lemon juice, zest and 1/2 teaspoon salt together in a medium bowl.
Fold pistachio mixture into labneh, leaving mixture marbled. Top with remaining pistachios, mint leaves and dill sprigs.